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A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution

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  • Mahmutoğulları, Özlem
  • Yaman, Hande

Abstract

The inventory routing problem arises in vendor managed systems, in which a supplier is responsible for replenishing inventories of products at a set of retailers and manages the logistics over a finite planning horizon with a fleet of capacitated vehicles. We consider this problem in the context of the distribution of two different quality products with one-way product substitution, where the high-quality product may be used to meet the demand for the low-quality product. The routes of vehicles and the quantities of products sent to each retailer in each period are determined in such a way that no stockouts occur and the total cost associated with inventory holding, substitution and transportation is minimized. In this study, we derive a mixed integer linear programming formulation for the problem, strengthen this formulation with valid inequalities and develop a branch-and-cut algorithm as an exact solution method. We conduct experiments using benchmark and randomly generated instances to analyze the effectiveness of our solution method and investigate the relationship between product substitution decisions and system costs under different demand, supply, vehicle capacity and substitution cost settings.

Suggested Citation

  • Mahmutoğulları, Özlem & Yaman, Hande, 2023. "A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution," Omega, Elsevier, vol. 115(C).
  • Handle: RePEc:eee:jomega:v:115:y:2023:i:c:s0305048322001591
    DOI: 10.1016/j.omega.2022.102752
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    References listed on IDEAS

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    1. Fokkema, Jan Eise & Land, Martin J. & Coelho, Leandro C. & Wortmann, Hans & Huitema, George B., 2020. "A continuous-time supply-driven inventory-constrained routing problem," Omega, Elsevier, vol. 92(C).
    2. Christiansen, Marielle & Fagerholt, Kjetil & Flatberg, Truls & Haugen, Øyvind & Kloster, Oddvar & Lund, Erik H., 2011. "Maritime inventory routing with multiple products: A case study from the cement industry," European Journal of Operational Research, Elsevier, vol. 208(1), pages 86-94, January.
    3. Arthur Hsu & Yehuda Bassok, 1999. "Random Yield and Random Demand in a Production System with Downward Substitution," Operations Research, INFORMS, vol. 47(2), pages 277-290, April.
    4. Cárdenas-Barrón, Leopoldo E. & Melo, Rafael A., 2021. "A fast and effective MIP-based heuristic for a selective and periodic inventory routing problem in reverse logistics," Omega, Elsevier, vol. 103(C).
    5. Freeman, Nickolas & Mittenthal, John & Keskin, Burcu & Melouk, Sharif, 2018. "Sourcing strategies for a capacitated firm subject to supply and demand uncertainty," Omega, Elsevier, vol. 77(C), pages 127-142.
    6. Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2012. "Robust Inventory Routing Under Demand Uncertainty," Transportation Science, INFORMS, vol. 46(3), pages 327-340, August.
    7. Manousakis, Eleftherios & Repoussis, Panagiotis & Zachariadis, Emmanouil & Tarantilis, Christos, 2021. "Improved branch-and-cut for the Inventory Routing Problem based on a two-commodity flow formulation," European Journal of Operational Research, Elsevier, vol. 290(3), pages 870-885.
    8. Archetti, Claudia & Speranza, M. Grazia & Boccia, Maurizio & Sforza, Antonio & Sterle, Claudio, 2020. "A branch-and-cut algorithm for the inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 282(3), pages 886-895.
    9. R. Kipp Martin & Linus Schrage, 1985. "Subset Coefficient Reduction Cuts for 0/1 Mixed-Integer Programming," Operations Research, INFORMS, vol. 33(3), pages 505-526, June.
    10. Bertazzi, Luca & Coelho, Leandro C. & De Maio, Annarita & Laganà, Demetrio, 2019. "A matheuristic algorithm for the multi-depot inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 524-544.
    11. Pochet, Y. & Wolsey, L. A., 1994. "Polyhedra for lot-sizing with Wagner-Whitin costs," LIDAM Reprints CORE 1129, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Anantaram Balakrishnan & Joseph Geunes, 2000. "Requirements Planning with Substitutions: Exploiting Bill-of-Materials Flexibility in Production Planning," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 166-185, January.
    13. Alvarez, Aldair & Cordeau, Jean-François & Jans, Raf & Munari, Pedro & Morabito, Reinaldo, 2021. "Inventory routing under stochastic supply and demand," Omega, Elsevier, vol. 102(C).
    14. Li, Yongjian & Chen, Jian & Cai, Xiaoqiang, 2007. "Heuristic genetic algorithm for capacitated production planning problems with batch processing and remanufacturing," International Journal of Production Economics, Elsevier, vol. 105(2), pages 301-317, February.
    15. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    16. Yehuda Bassok & Ravi Anupindi & Ram Akella, 1999. "Single-Period Multiproduct Inventory Models with Substitution," Operations Research, INFORMS, vol. 47(4), pages 632-642, August.
    17. Coelho, Leandro C. & Laporte, Gilbert, 2014. "Improved solutions for inventory-routing problems through valid inequalities and input ordering," International Journal of Production Economics, Elsevier, vol. 155(C), pages 391-397.
    18. Yossiri Adulyasak & Jean-François Cordeau & Raf Jans, 2014. "Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 103-120, February.
    19. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    20. G. R. Bitran & S. Dasu, 1992. "Ordering Policies in an environment of Stochastic Yields and Substitutable Demands," Operations Research, INFORMS, vol. 40(5), pages 999-1017, October.
    21. M. W. Padberg & T. J. Van Roy & L. A. Wolsey, 1985. "Valid Linear Inequalities for Fixed Charge Problems," Operations Research, INFORMS, vol. 33(4), pages 842-861, August.
    22. Walter J. Bell & Louis M. Dalberto & Marshall L. Fisher & Arnold J. Greenfield & R. Jaikumar & Pradeep Kedia & Robert G. Mack & Paul J. Prutzman, 1983. "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces, INFORMS, vol. 13(6), pages 4-23, December.
    23. Piñeyro, Pedro & Viera, Omar, 2010. "The economic lot-sizing problem with remanufacturing and one-way substitution," International Journal of Production Economics, Elsevier, vol. 124(2), pages 482-488, April.
    24. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    25. Padberg, M.W. & Van Roy, T.J. & Wolsey, L.A., 1985. "Valid linear inequalities for fixed charge problems," LIDAM Reprints CORE 656, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Claudia Archetti & Luca Bertazzi & Gilbert Laporte & Maria Grazia Speranza, 2007. "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transportation Science, INFORMS, vol. 41(3), pages 382-391, August.
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